2.5 Conductors

Materials „ Materials made up of normal matter (atoms, molecules, etc.) have some amazing electromagnetic properties! „ Simplest kinds of electromagnetic properties: „conductor (of electricity) „partial conductor/insulator „non-conductor insulator „ Why materials conduct vs. do not conduct electricity depends on microscopic (i.e. quantum) structure of materials & temperature (i.e. thermal/internal energy).

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CONDUCTORS „ "normal" good conductors of electricity: – metals - gold, platinum, silver, copper... – Have finite DC resistance, R = V/I (Ohm’s Law) @ finite temperatures, T > 0 K

„ "superconductors“ – low temperature SC's such as lead ( Tc~4K) indium, niobium, ..... – Hi- TC SCs (e.g. Tc~77K): BSCO, YBCO ..... – DC resistance vanishes below Tc (critical temp)

„ An perfect conductor is a (hypothetical) material that would have an unlimited number of completely free electrons/free charges. No such things truly exist in nature, but ∃ many materials which do come (amazingly) close to an ideal/perfect conductor. EM-2.5-2

„ INSULATORS: – e.g. plastics, teflon, glass, rubber ….

„ PARTIAL CONDUCTORS: – e.g. doped plastics, semi-conductors (germanium, silicon, graphite….)

„ IONIC LIQUIDS: – e.g. salt water – can also conduct electricity – Acidic solutions – ions transport electrical charges – not electrons

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Properties of a conductor 1. ENET(r) =0 inside a conductor 2. The volume free charge density = 0 inside a conductor 3. Any induced charges on a conductor can ONLY reside on surface(s) of the conductor– as surface charge distributions 4. The entire volume & surface of a conductor is an equipotential 5. Just outside the surface of a conductor, E(r) is perpendicular/normal to the surface

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Example

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Example (conti.)

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Example (conti.)

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Obtain free charge from V or E „ We have derived, using Gauss’ Law: or „ From Griffiths Eqn’s 2.34-2.37, p. 89-90:

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FORCE & PRESSURE ON A CONDUCTOR

„ Edge on view

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FORCE & PRESSURE ON A CONDUCTOR (conti.) „ We have discussed that 1. A surface charge has a net E ┴ to surfaces both sides. 2. E=0 inside a conductor. „ What happens? „ Consider the patch removed

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FORCE & PRESSURE ON A CONDUCTOR (conti.) „ What is the force/pressure acting on the patch?

„ sum up all the “patches” associated with the conducting surface

„ Pressure=force/area

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CAPACITORS „ A capacitor is a device that enables the storage of electric charge, Q. „ Since there are electric fields associated with electric charge, a capacitor is also a device that enables the storage (long and/or short term) of electrical energy.

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CAPACITORS (conti.)

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CAPACITORS (conti.) „ Using Gauss’ Law on the upper plate

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EXAMPLE 2.11 „ Find the capacitance, C of two concentric spherical metal shells, with radii a & b, b > a.

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Work done in charging up a capacitor „ Charging an initially uncharged capacitor means individually removing electrons from the upper plate of the parallel-plate capacitor (inner sphere of concentric spherical capacitor) and transporting them to the lower plate of the parallel-plate capacitor (outer sphere of concentric spherical capacitor), respectively.

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